The irony is that although the Wrights invented some fundamental analysis of lift and drag, and I think were the first to make a wind tunnel, they were fixated on getting that permanent patent on flight, and when others came along after them they had difficulty asserting their prior art. Their only proof of their initial flight was an article in a newspaper which they were initially unhappy was published.
Ironically, their approach to the problem of flight was quite limited, and advances by Glenn Curtis and others quickly transcended all of the Wrights technology. To such an extent that nothing unique to the Wrights design remains in use.
Basically their achievement constituted proof-of-concept which legitimated the efforts of Curtis and others. Less the beginning of flight as we know it than the end of the presumption that powered, heavier-than-air flight was not possible.
It is easy to see that powered flight only works when you have a light enough power plant generating enough power; the Wrights design successfully finessed the limitations of a marginally good-enough power plant. One of the ways they did it was with the twisted propeller, shaped the way you see a rubber-band powered model aircraft propeller is shaped. That milked the most thrust out of their marginal power plant for the low speed flight regime. Another such decision is their canard pitch control, which provides positive lift rather than a negative lift as in conventional horizontal tail design. It works - at low speed. Which is the only regime their engine was ever going to take them. At high speed, such a design is hopelessly unstable (in the absence of sophisticated technology to control it). The Wrights depended on being low and slow enough that the instability crashes would be survivable.
The Wrights achievement is impressive. But they solved the problem of flying at all, without doing much in the way of power plant development. In retrospect their design is a quaint backwater from the time when engines adequate to high and fast flight did not yet exist.
Well NASA has been experimenting with wing warping on a modified F-18. Perhaps their ideas were too far ahead of their time to be practical.
http://www.nasa.gov/centers/armstrong/news/FactSheets/FS-061-DFRC.html#.VJINWIdCoiU